Q. Two wires of the same material and radii $r$ and $2r\ $respectively are velded together end to end. The combination is used as a sonometer wire and kept under tension$T$. The welded point is midway between the two bridges. When stationary waves are set up in the composite wire, the joint is a node. Then the ratio of the number of loops formed in the thinner to thicker wire is
A) 2:3
B) 1:2
C) 2:1
D) 5:4
Explanation
(b) $n = \frac{p_{1}}{lD_{1}}\sqrt{\frac{T}{\pi\rho}} = \frac{p_{2}}{lD_{2}}\sqrt{\frac{T}{\pi\rho}}$
$\therefore\frac{p_{1}}{D_{1}} = \frac{p_{2}}{D_{2}}$
$\frac{p_{1}}{p_{2}} = \frac{D_{1}}{D_{2}} = \frac{2(r)}{2(2r)} = \frac{1}{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.